Provide a glimpse of some widely used matrix factorizations, some of which are discussed later in the text.
(Singular Value Decomposition) Suppose A = UDV T, where U and V are n X n matrices with the property that UTU = I and VTV = I, and where D is a diagonal matrix with positive numbers σ1,,,,,,,,,σn on the diagonal. Show that A is invertible, and find a formula for A-1